The backbone of President Obama’s health care law is taking shape, with 26 states choosing to let the federal government run the online insurance markets mandated by his signature reforms instead of keeping the job in-house or partnering with the feds.

The Department of Health and Human Services had encouraged states to run their own markets, or “exchanges,” that help the uninsured find coverage. Only 17 states and the District of Columbia took on the task, while seven states decided to split the duty with the Obama administration, according to a breakdown by the Kaiser Family Foundation.

The exchanges, which are designed to let those without employer-based insurance compare and buy plans with the help of tax credits, are a crucial part of the Patient Protection and Affordable Care Act that passed in 2010 and largely was upheld by the Supreme Court in June. States that wanted to run a partnership exchange with the federal government had to let HHS know by late Friday, ending months or even years of debate among governors and state lawmakers.

Their discussions marked one of two major decisions under “Obamacare.” Whether or not to expand Medicaid within their borders is the other, and it remains a source of contention in state capitals across the country.

The Obama administration says it will be ready to run exchanges in more than half the states, even though a bevy of Republican governors and lawmakers flouted their intentions by saddling them with the task.

“It’s not what the drafters of the bill had hoped would happen,” Timothy Jost, a health law expert at Washington and Lee University School of Law, said of the outcome on Friday.

State leaders who deferred to the federal government cited numerous reasons for their choices: They wanted to distance themselves from Mr. Obama’s first-term achievement, could not obtain enough information to make an informed decision or ran out of time after Mitt Romney lost the presidential election. That loss effectively ended Republicans’ hopes to repeal the health care law.

New Jersey Gov. Chris Christie sent a letter to HHS Secretary Kathleen Sebelius on Friday to confirm his previously stated preference for a federally run exchange.

West Virginia, meanwhile, applied for a partnership exchange “to retain our ability to assist consumers and maintain our traditional authority to regulate health insurance” in the state, said Jeremiah Samples, an official at the West Virginia Insurance Commission. He said that after months of analysis, officials decided that a state-run exchange would not be worth it because of the state’s relatively small market and the hefty information-technology costs associated with the exchange.

From the start, HHS advised states to run the exchanges so they could tailor them to their residents’ needs. But the majority said no.

Mr. Jost said the tilt toward federally run exchanges may help officials in Washington stay on the same page during the early stages of implementation because the marketplaces rely on computer networks that will share data among several federal agencies.

“It’s not a particularly bad thing at this point to be doing it this way,” Mr. Jost said.

Federal health officials declined to comment on the states’ decisions before midnight Friday, making it unlikely they will weigh in on the spectrum of exchanges until early this week.

The Obama administration is striking an optimistic tone less than eight months before enrollment begins, despite the burden of implementation.

“We are making great progress, we are on track, and we will be ready for people all across the country to obtain high-quality, affordable health care coverage beginning on Oct. 1,” Gary Cohen, director of the Center for Consumer Information and Insurance Oversight, told the Senate Finance Committee on Thursday.

States that deferred to a federally run exchange can change their minds and apply later this year to run their exchange in 2015, an option that will remain available in succeeding years, Mr. Cohen said.